From Daniel's initial location from the campsite given the width of the
stream is 400 feet and Daniel swims to the boat ramp, we have;
1.) Please find attached the drawing of the situation
2.) 3.34 minutes
3.) 1,298.59 feet
4.) 3.69 minutes
How can the distances and times be calculated?
1.) Please find attached a labelled diagram of the scenario created with MS Visio
2.) Daniel's average swimming rate (speed) = 150 feet per minute
[tex]The \ distance \ Daniel \ swims = \mathbf{\dfrac{400 \, feet}{sin(53^{\circ})}} \approx 500.85 \, feet[/tex]
The time it takes him to swim to the boat ramp, t, is therefore;
- [tex]t \approx \dfrac{500.85 \ feet}{150 \ feet/min} \approx \underline{3.34 \ minutes}[/tex]
3.) The distance, d₁, downstream of the boat ramp from Daniel is given as follows;
d₁ = √((500.85 feet)² - (400 feet)²) ≈ 301.41 feet
Therefore;
The distance from the boat ramp to the campsite, d₂, is therefore;
d₂ ≈ 1600 feet - 301.41 feet = 1,298.59 feet
The distance from the boat ramp to the campsite, d₂ ≈ 1,298.59 feet
4. The time, t₂, it will take Daniel to jog from the boat ramp to the campsite is given as follows;
[tex]t_2 = \mathbf{\dfrac{d_2}{v_2}}[/tex]
Where;
v₂ = The rate at which Daniel can jog, which is 4 mph
Which gives;
[tex]t_2 = \mathbf{\dfrac{1298.59 \, feet}{4 \, mph}} = \dfrac{1298.59 \, feet}{4 \, mph} \approx \dfrac{1298.59 \, feet}{5.866142 \ feet/s} \approx \dfrac{221.37 \, s}{60 \, s/min} \approx 3.69 \, min[/tex]
Therefore;
- The time it takes him to jog from the boat camp to the campsite, t₂ ≈ 3.69 minutes
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